the lorenz equations define a classic chaotic dynamical system. any orbit meanders about an attractor in a way that, though deterministic, appears impossible to predict.
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being chaotic, the lorenz system exhibits SDIC = sensitive dependence on initial conditions. if you start multiple orbits very close to one another, they will eventually diverge and have independent long-term behaviors.
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the lorenz system has an *attractor*, meaning that all initial conditions, if integrated for a long-enough time, will eventually evolve onto the attractor. such a chaotic attractor is often called "strange".
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this last vid is in the style of work of @thespite, who has a very nice series of inky strange attractors, with links to code available: e.g.,
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